Question

The sum of n terms of an AP is 3n² + 5n. Find the AP. Hence find its 15th term.

Answer 1

Sn = 3n^2 + 5n

Sn – 1 = 3(n – 1)^2 + 5(n – 1)

= 3(n^2 + 1 – 2n) + 5n – 5

= 3n^2 + 3 – 6n + 5n – 5

= 3n^2 – n – 2

an = Sn – Sn – 1 = 3n^2 + 5n – (3n^2 – n – 2)

= 6n + 2

AP is 8, 14, 20, ....................

a(15) => a + 14d = 8 + 14(6) = 92